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It's a 5/4/3/2 weighted average, with "2" as the regression-to-the-mean weight. In my spreadsheet, this means that I'm adding a regression component to the weighted mean of the Fangraphs and B-Ref batting, baserunning, and fielding numbers, but not to the replacement level and positional adjustments.

Based on the fact that runs scored per game dropped under 10 this year, I'm using a factor of 9.7 runs per win. Based on a guess projection of low salary inflation, I calculate projected $$ value at $4.6M per win.

I am assuming, looking over this, that Fielder will get a very large contract. If he's available for much less than Pujols, he becomes a more attractive option in theory. Even then, though, I really hate the idea of dropping that much money on a guy who's already a DH and is kind of a big fatty.

I also think these numbers suggest that Theo will make a big, big play to bring Pujols to Chicago.

Why do Fielder and Pujols have different positional adjustment numbers?

1) Fielder has played slightly more games overall, so he has both a higher replacement level adjustment and a lower positional adjustment.
2) Pujols has played a couple games at 3B, and has DH'd in interleague once. Fielder has DH'd several games.
3) The difference appears larger than it really is due to rounding. If I went to one decimal place, it'd be -10.5 for Pujols and -11.6 for Fielder.

I just realized I shouldn't use the same positional adjustment for all of these players, in the DH projections, since the players who play fewer games would have fewer positional runs deducted. You can add about three runs to the projections for Willingham and Ramirez. That makes Willingham over Ortiz a tremendous no-brainer. (Unless you are exceptionally confident that Ortiz' 2009 off year shouldn't affect his projection.)

Would a Pujols/Gonzalez DH/1B split time work? I have a hard time believing it would, simply because I can't recall the last time two genuinely great 1B (at least from an offensive POV) split time between 1B and DH. It's a stretch to think Pujols would go for that, especially when he could likely have just as much $ and play 1B full-time (and likely in the NL, where he'd be more comfortable).

At his first press conference, Cherington said that he expected Kalish and Reddick to compete for the RF job. I think it makes sense for the Sox to go cheap in right - they'll need an RHB caddy - and hope one or both of the kids develop. I don't like the idea of signing a free agent who blocks both of the club's best prospects.

The problem with Pujols is going to be the length of the contract, not the AAV. He's pretty clearly worth $25M+ now and probably for the next 2-3 years. After that, though? (Pregnant pause.)

I think Fielder makes more sense than Pujols for the Sox. But I wouldn't sign him either. He's oscillated between being a 130 OPS+ guy and a 165 OPS+ guy, and if recent history has taught us anything it's that the Sox would most assuredly be getting the 130 OPS+ guy if they sign him for big bucks. Also, you'd have to wonder if being a full-time DH would reduce the incentive for Prince to keep his weight under control.

It seems pretty clear to me that the club's money would be better spent on pitching. Then use whatever's left to try to bring back Ortiz or sign Willingham to DH.

And a piece of news I missed - Sox picked up Scutaro's option yesterday - that sets us up for a mostly Redemption Plan offense. While trades are possible, it looks most likely that we'll see Reddick/Kalish take over RF and a new DH. I guess it could be Ortiz, but I have trouble seeing him being worth the money compared to cheap options like Willingham.

A right-handed DH who could cover an outfield corner and possibly play some 3B in a pinch fits the Sox roster pretty well. I'm guessing the market for Cuddyer this offseason will be very light, and he's the sort of guy who might be had for 2/8 or so. Not my first choice, but a possibility for the sox.

The Red Sox are in active negotiations with Ortiz and there is a possibility he could sign prior to entering the market. There is virtually no chance that will happen with Papelbon, who has long been intent on entering the market and told the Red Sox that.

PeteAbe had the above note in the Extra Bases post about Mackinin and Sveum yesterday. Maybe I'm overreading it but I wonder if he has a source that tells him that they are moving forward on Ortiz and that a deal is likely or is he just guessing?

I like the Cuddyer idea. Just generally who is out there as a fourth outfielder who is both good enough to jump in as a regular but not so accomplished to be expecting a regular job? Cody Ross looks like a guy who might fit the bill there.

I think Cuddyer's value lies more in his versatility than anything. He's a decent bat that you can play just about anywhere. No, his glove work won't be good anywhere, but he can still fill in all over the place. Honestly he'd be a really good fit on a team like the Yankees where he could split DH/RF/3B with ARod and Swisher. The Red Sox make sense in this vein too, although Fenway's RF would be disastrous for Cuddyer, whereas the tiny RF at NYS wouldn't really expose his lack of range.

I just realized I shouldn't use the same positional adjustment for all of these players, in the DH projections, since the players who play fewer games would have fewer positional runs deducted. You can add about three runs to the projections for Willingham and Ramirez. That makes Willingham over Ortiz a tremendous no-brainer. (Unless you are exceptionally confident that Ortiz' 2009 off year shouldn't affect his projection.)

Why would you project Willingham differently than Ortiz assuming they would be the starting DH? Are you suggesting that Willingham would get hurt and that would positively affect his value to the team? I'm missing something here...

Why would you project Willingham differently than Ortiz assuming they would be the starting DH?

The projection includes a playing time component. Willingham, having played fewer games over the last three years than Ortiz, projects to play fewer games in 2012 as well.

The positional adjustment is based on position played and playing time. If someone who starts a full seasons of games at 1B would have a -10 positional adjustment, then someone who missed the first half of the season and then played a half season at 1B would have a -5 positional adjustment. In the numbers in the original post, I used the same positional adjustment for all the players, regardless of projected playing time. That was wrong - the projected positional adjustment for potential DHs should be adjusted for their projected playing time.

I personally prefer that the Sox let Ortiz walk and sign Beltran as a DH/ RFer and collect the draft picks (assuming that the comp picks for this off-season still follow the CBA from last year). If whoever of Kalish/ Reddick struggles too much Beltran can be shifted in RF (or against a tough LHP) with Youk going to DH and Lowrie/ Avilles covering 3B.

I think Cuddyer's value lies more in his versatility than anything. He's a decent bat that you can play just about anywhere. No, his glove work won't be good anywhere, but he can still fill in all over the place. Honestly he'd be a really good fit on a team like the Yankees where he could split DH/RF/3B with ARod and Swisher.

But, can he play 3B?

Montero's getting a majority of the DH time. You'd have to be comfortable giving Cuddyer 60 games at 3B.

I personally prefer that the Sox let Ortiz walk and sign Beltran as a DH/ RFer and collect the draft picks (assuming that the comp picks for this off-season still follow the CBA from last year). If whoever of Kalish/ Reddick struggles too much Beltran can be shifted in RF (or against a tough LHP) with Youk going to DH and Lowrie/ Avilles covering 3B.

Seems like a good idea, assuming Ortiz's and Beltran's contracts would be at all similar, but I doubt Beltran wants anything other than a reasonable guarantee that he'll play the field in 90% of his next team's games.

I think Pujols/Fielder get lumped together because, while it's clear Pujols is a better player, he's (slightly) older. I agree with you that they shouldn't be thought of as interchangeable. While either may fall off a cliff, Pujols has 11 years of inner-circle performance while it looks to me like Fielder is yet another in a long line of guys who look are superstars for a few years, legitimately, and then decline fairly rapidly. That is, if I had to bet who would still be worth close to their contracts at the end of it, my money is on Pujols over Fielder despite the age difference and likelihood that Pujols gets more years.

I don't see him as any kind of fit in Boston, though, without either trades or undue roster disruption. For the right price, Fielder might make a fine DH choice. I doubt Pujols would want to move off 1B.

The positional adjustment is based on position played and playing time. If someone who starts a full seasons of games at 1B would have a -10 positional adjustment, then someone who missed the first half of the season and then played a half season at 1B would have a -5 positional adjustment. In the numbers in the original post, I used the same positional adjustment for all the players, regardless of projected playing time. That was wrong - the projected positional adjustment for potential DHs should be adjusted for their projected playing time.

I don't know why I'm having such a difficult time grasping this concept, but I am. What you're saying is that the guy who plays fewer games is more valuable -- fewer negative runs -- than the guy who plays more games. I guess I'm confused as to why this adjustment takes place in the positional part of WAR, as opposed to the fielding defense portion. I can see it making sense for defense (although the DH part also throws a bit of a wrench in here, too) -- more games for a poor fielder, more accumulation of 'negative' runs -- but like I said, I can't wrap my head around the positional adjustment. Can you try and explain it a little differently?

I can't wrap my head around the positional adjustment. Can you try and explain it a little differently?

To expand on what JJ said -

Think of the numbers this way. First you have Batting runs, which are calculated simply relative to league average. For every run better (with the bat) than an average player you are, you get a run, for every run worse, you lose a run. Baserunning and Fielding runs work the same way.

Second, obviously, an average player doesn't have 0 value. The Replacement Level adjustment now gives players credit for their playing time - it's the difference between replacement level and average. Over a full seasons, an average player is about 20 runs better than a replacement level player. So you get players who play a full season getting a +20 replacement level adjustment, and players who play less than a full season getting a somewhat lower replacement level adjustment. (A true replacement level player, who gets a full season of playing time, will get a +20 replacement level adjustment, but will also have a -20 value above average, to even it out.)

Third, you have to adjust for position. An average (or replacement level) shortstop hits worse than an average (or replacement level) 1B. This adjustment also has to be relative to playing time - an average SS is 15-20 runs worse than an average 1B over a full season, so he's only 7-10 runs worse over a half season.

My mistake in the above calculations was that I didn't adjustment the DH position adjustment for playing time. The DHs who project to play a full season of games should have a larger positional adjustment than the DHs who project to play less than a full season of games.

As JJ says, this doesn't mean that it's better for a DH to play fewer games - the positional adjustment is smaller than the replacement level adjustment. I had already given the 150 game DHs credit for their projected durability in the Replacement level adjustment, but I should have made the (somewhat smaller) positional adjustment relative to projected playing time as well.

That's as a RF, correct? As a DH, I think he would be somewhere around +18 runs and $9M, between Willingham and Ortiz. (EDIT: Does that sound about right? EDIT2: Actually, if I do a reduced positional adjustment it might be +23R, $11M, right at Ortiz level.)

Granted, he's hitting the market as a RF. And granted, he played 142 games in 2011 after a couple of major-injury years. But if you can argue a RHB in Willingham is better than a LHB in Ortiz, you could make the argument that a BHB in Beltran, plus someone who could be at least competent in the field, would be even better. Putting Beltran in a transitional role as RF/DH, splitting time with Kalish and/or Reddick in both spots, could work.

The drawback - and I have to state it before I go all-in on irrationalization - is that you might overpay both in AAV and years for Beltran. On AAV, it would be for paying RF prices for a DH; on years, anything beyond 2 is a major risk for a player with his injury history. Heck, one could argue that even 1 year is an unacceptable injury risk. But the market is also aware of his injury history, and his age. If the market has the same trepidation with Beltran that they did with Beltre (after Seattle), Boston might be able to put together an acceptable offer to both sides.

Granted, he's hitting the market as a RF. And granted, he played 142 games in 2011 after a couple of major-injury years. But if you can argue a RHB in Willingham is better than a LHB in Ortiz, you could make the argument that a BHB in Beltran, plus someone who could be at least competent in the field, would be even better. Putting Beltran in a transitional role as RF/DH, splitting time with Kalish and/or Reddick in both spots, could work.

willingham wouldn't cut it in rf, right? beltran makes a ton of sense to me. you could essentially platoon reddick or kalish with lowrie or aviles with youk and beltran splitting time between 3b/rf and dh. to me, a huge key to 2012 will be to get right handed bats that can stay in the lineup, and the easiest way to do that is to open up the dh spot, at least part of the time. as good a hitter as ortiz is, i just don't see a spot for him on this club any more.

I just don't think the numbers work out to Papi being the best DH option for the Red Sox this offseason. Willingham projects as just about the same player, but right-handed and a good deal cheaper. Beltran projects as just about the same player, but with a good glove in RF.

I'd be okay with bringing back Ortiz as long as the money is reasonable. I really think Pujols or even Fielder are worth the larger cash outlay, but if the money isn't there (or the interest in the role they'd play in Boston), then Ortiz is probably the way to go. I don't think Willingham is going to be as cheap as people think; someone is going to pay him to be an outfielder. Beltran is interesting, but the issue is that if you want to put him in RF, and shift Youk to DH, this team doesn't have great options to play third, and you're looking at downgrading from Reddick/Kalish/Platoon partner to Aviles/Lowrie on offense (while also giving Scutaro more ABs at SS since you're taking these guys and putting more of their PT at 3B).

The thing about Willingham is that he's a pretty bad outfielder. His value there isn't much different than it would be at DH. I still like Ortiz better, mainly for sentimental reasons. I like Beltran better too but I guess he'll cost a lot more.

but the issue is that if you want to put him in RF, and shift Youk to DH, this team doesn't have great options to play third, and you're looking at downgrading from Reddick/Kalish/Platoon partner to Aviles/Lowrie on offense (while also giving Scutaro more ABs at SS since you're taking these guys and putting more of their PT at 3B).

there are two things missing here. the first is that i think youk has shown that he has trouble staying healthy, especially last year when he was asked to play 3b. so, the option to have him dh should keep his bat in the lineup. second, the beltran option provides sort of a mirror image of youk, but in right. iow, he should also be able to stay in the lineup more if the dh option is available.

now, this all falls apart if they both need to dh for some reason, but this also falls apart if ortiz or another dh-only type is on the roster. with youk and beltran dh-ing part time, you only have to play lowrie/aviles part time at third. of course, you'd rather have them as backups ... so, having youk play every day at 3rd looks good on paper, but in practice, it's likely to end up as either lowrie or aviles being the full time 3b for september again.

expecting youk to play 140 games at 3rd is foolish, so if they want his bat in the lineup every day, they are going to have to choose between him or ortiz.

How often is this really done? Give a guy rest by having him DH? I only really watch the Sox, so it's an honest question.

i was surprised that arod hasn't gotten more time at dh--10 games last year, 12 the year before. vlad guerrero got a lot of time at dh in his last few years in anaheim--30 in 06, then 41, then 44, before becoming a full time dh (when he could even do that) in 09. joe mauer had been dh-ing in his days off behind the plate before this past year's disaster. i think the most interesting case is michael young, who dh-ed in 69 games this past year--less than a half of the season--and saw his offensive numbers spike.

the michael young case is interesting not only b/c of the offenseive spike, but also b/c of youk's positional flexibility. tell him to bring his 3b and 1b gloves to the park every day and be ready to fill in if need be, but that the most important thing he can do for the team is to be healthy enough to hit every day. combine that with a few role players that can hit a little if you play the matchups right, and i think it could work really well.

Beltran is interesting, but the issue is that if you want to put him in RF, and shift Youk to DH, this team doesn't have great options to play third, and you're looking at downgrading from Reddick/Kalish/Platoon partner to Aviles/Lowrie on offense (while also giving Scutaro more ABs at SS since you're taking these guys and putting more of their PT at 3B).

The idea was that Beltran would switch between RF and DH, with Reddick/Kalish taking the opposite. It didn't involve Youk at all.

Are we now officially establishing that 3B is a need? That probably warrants a completely separate thread. If 3B is a need, then it would seem either that Youkilis becomes the DH - which shifts the solution away from Beltran entirely - or Youkilis should be traded. The other alternative is to get a backup who can share time, but I don't think we want to go get, say, Scott Rolen and have a repeat of Mike Lowell 2010. In concept it's easy to define what they need, but in reality it's beyond impractical to arrange something ideal.

The idea was that Beltran would switch between RF and DH, with Reddick/Kalish taking the opposite. It didn't involve Youk at all.

I think most people have assumed that if either of Reddick or Kalish gets the RF job, he would need to be platooned. If you add Beltran and have him split time between RF and DH, then you can either platoon at DH or at whatever position the new part-time DH plays.

our top prospect plays 3b, so it's not a long term need, but i think given youk's injury track record, having a good backup there is a short term need. fortunately, we have aviles and lowrie on hand, so i think everything sort of works out.

The thing about Willingham is that he's a pretty bad outfielder. His value there isn't much different than it would be at DH. I still like Ortiz better, mainly for sentimental reasons. I like Beltran better too but I guess he'll cost a lot more.

Willingham's certainly below average in the OF, but he's not horrible. He has a career -5 UZR/150 and -3 TZ/150 in the OF, and his arm seemed strong enough that he could play RF. A -5 OF is about a full win more valuable than a DH who can't play the field.

The other consideration is the draft picks--the Sox would lose a first rounder for Willingham, but likely gain a first rounder and a sandwich pick for Ortiz.